Organize the information from the text in the form of a mind map or a flow chart. For example, types properties
Compare your mind map with your partner’s.
Fractals
A fractal is generally a rough or fragmented geometric shape that can be split into parts, each of which is a miniature replica of the whole. Roots of mathematical interest in fractals can be traced back to the late 19th century; however, the term "fractal" was coined by the French mathematician Benoît Mandelbrot in 1975 from the Latin fractus meaning "broken". Fractals connote fraction, fracture and fragment. 1) …. A mathematical fractal is based on an equation that undergoes iteration, a form of feedback based on recursion.
2)…. The fractal dimension, D, is a statistical quantity that gives an indication of how completely a fractal appears to fill space, as one zooms down to finer and finer scales. Mathematicians tend to rank fractal dimensions on a series of scales between 0 and 3. One-dimensional fractals (such as a segmented line) typically rank between 0.1 and 0.9, two-dimensional fractals (such as a shadow thrown by a cloud) between 1.1 and 1.9, and three-dimensional fractals (such as a mountain) between 2.1 and 2.9. 3) .… Some studies in perceptual psychology have found that people prefer fractal dimensions similar to those found in nature.
Fractals can be deterministic or stochastic. They can also be classified according to their self-similarity. There are three types of self-similarity found in fractals:
Exact
self-similarity: the fractal appears identical at different scales.
Fractals defined by iterated function systems often display exact
self-similarity.
Quasi-self-similarity: quasi-self-similar fractals contain small copies of the entire fractal in distorted and degenerate forms. Fractals defined by recurrence relations are usually quasi-self-similar.
Statistical self-similarity: the fractal has numerical or statistical measures which are preserved across scales. Random fractals are examples of fractals which are statistically self-similar.
4) ….
Because they appear similar at all levels of magnification, fractals are often considered to be infinitely complex. Natural objects that are approximated by fractals to a degree include clouds, mountain ranges, lightning bolts, river networks, coastlines, snowflakes, various vegetables and plants, animal coloration patterns, neurons, the respiratory and circulatory systems. 5) ….
Fractal geometry is a powerful tool for uncovering secrets from a wide variety of systems and solving important problems in applied science. 6) …. Fractal analysis is now widely used in all areas of science, such as astrophysics, medicine, meteorology, architecture, study of soils, seismology, enzymology, computer graphics, biology, robotics, economics, finance, engineering, and even music. Fractal principles are also at work in arts or crafts, such as some Dalì and Pollock paintings, works of Maurits Escher, mandalas, mosaics, tiling designs, and floor decorations.
Fractals are purely a wonder – too irregular to be described by Euclidean geometry; iterative and recursive and seemingly infinite.